Mrs. Hernandez owns a computer training business. She charges a lab fee plus an hourly fee to train office workers on various software programs. It costs $265.00 to attend a 6-hour course and $345.00 for an 8-hour course. Which equation relates x, the number of hours in the course, and y, the cost?

Question

Mrs. Hernandez owns a computer training business. She charges a lab fee plus an hourly fee to train office workers on various software programs. It costs $265.00 to attend a 6-hour course and $345.00 for an 8-hour course. Which equation relates x, the number of hours in the course, and y, the cost?

Answer 1

y=ax+b

8a+b = 345
6a+b = 265
2a = 80
a=40
b=25

y = 40x+25

Answer 2

To determine the equation that relates the number of hours in the course (x) and the cost (y), we need to identify the mathematical relationship between these variables. In this scenario, the cost consists of two components: a lab fee (fixed cost) and an hourly fee (variable cost).

Let's break down the given information:

For a 6-hour course, the cost is $265.00.
For an 8-hour course, the cost is $345.00.

To find out the hourly fee, we need to subtract the lab fee from the total cost and then divide the remaining amount by the number of hours.

For the 6-hour course:
Total cost (y) = Lab fee + Hourly fee * Number of hours
265 = Lab fee + Hourly fee * 6

For the 8-hour course:
Total cost (y) = Lab fee + Hourly fee * Number of hours
345 = Lab fee + Hourly fee * 8

Now, we have two equations with two unknowns (Lab fee and Hourly fee). By solving this system of equations, we can determine the relationship between the number of hours and the cost.

Let's solve these equations:

Equation 1: 265 = Lab fee + Hourly fee * 6
Equation 2: 345 = Lab fee + Hourly fee * 8

We can manipulate these equations to isolate either the Lab fee or the Hourly fee. One way is to subtract Equation 1 from Equation 2:

345 - 265 = Lab fee + Hourly fee * 8 - (Lab fee + Hourly fee * 6)
80 = Hourly fee * (8 - 6)

Simplifying:
80 = Hourly fee * 2

Now, divide both sides of the equation by 2:
80/2 = Hourly fee

Hourly fee = 40

Once we have the Hourly fee, we can substitute it into either Equation 1 or Equation 2 to find the Lab fee.

Let's use Equation 1:
265 = Lab fee + 40 * 6
265 = Lab fee + 240
Lab fee = 265 - 240
Lab fee = 25

Now we know the Hourly fee is $40 and the Lab fee is $25.

To summarize, the equation that relates the number of hours (x) and the cost (y) for Mrs. Hernandez's computer training business is:
y = 25 + 40x